I am reading the paper A geometric proof of the existence of Whitney stratifications. Theorem 1 states
Theorem 1. For any semivariety $V$ in $\mathbb{R}^m$ (or $\mathbb{C}^m$) there is an a- (resp. b-) regular stratification.
The first paragraph in proof of Theorem 1 says:
"A semivariety $V$ has well-defined dimension, say $d \leq m$. Denote by $V_{reg}$ the set of points, where $V$ is locally a real (or complex) analytic submanifold of $\mathbb{R}^m$ (or $\mathbb{C}^m$) of dimension $d$. $V_{reg}$ is a semivariety, moreover, $V_{sing} = V \setminus V_{reg}$ is a semivariety of positive codimension in $V$ , i.e., $\dim V_{sing} < \dim V$."
My question is: why $V_{sing}$ is a semivariety of positive codimension in $V$?